Even in Blackburn, on a crisp spring Saturday afternoon, Condoleezza Rice knew she couldn't escape the war - the Iraq war at least. Yet as the chants of a few hundred demonstrators periodically intruded yesterday, all was quiet on another front: the extraordinary battle shaping up back in America between the most powerful woman on earth and black America's most famous, and ferocious, film-maker.

And the reason Lee is so angry, and for the cyber-war which his increasingly barbed comments have ignited on blogsites countrywide, is the same one that inspired the Foreign Secretary, Jack Straw, to invite Rice to Liverpool and Blackburn: Condi as power politician. Much as she is seeking to dampen the speculation, there is a rising expectation that sooner or later she will become the first African American, and the first woman, to occupy the Oval Office.

Not if Spike Lee has his say. And since the beginning of this month, he has had lots to say on the matter. It all began with an interview in Stuff magazine in which he was talking about a documentary he is making on Hurricane Katrina. As the levees of New Orleans were collapsing, 'she was going up and down Madison Avenue buying Ferragamo shoes', he fumed, adding: 'I dislike Condoleezza Rice even more than Bush... She's gotten a free ride from black people.'

By last week he was in even fuller flow in an interview for the New York Observer, in which he said: 'African Americans will have to really, really, really, really, really, REALLY analyse the Secretary of State's record and get past the pigmentation of her skin. I'm not going to vote for that woman. No way!'

If Rice's Saturday in Blackburn is any indication, he may have a job stopping her. In a by-now-routine riposte that does not categorically close the door on a run for the presidency, she told a news conference she was looking forward to going back to supervising doctoral students at California's Stanford University.

The news conference was brief - sandwiched between a visit to Blackburn Cathedral, meeting Muslim community leaders, and a visit to the slave-trade exhibit at Liverpool's Maritime Museum - so there was no time allowed for a Spike Lee question. But if her fielding of challenges on Iraq, Guantánamo Bay and Muslim anger over US foreign policy were any indication, she would have deflected Spike's spikiness with a wide smile and a shrug of her (impeccably black-suited) shoulders.

Arriving at Blackburn town hall, she good-naturedly waved at some of the several hundred anti-war protesters. Once inside, she said: 'The protesters make my point. Democracy is the only system that allows people to be heard, and heard peacefully.' Besides, she'd been 'warmly' welcomed by an almost equally sizeable group of spontaneous well-wishers on her way - a point Straw, obviously enjoying himself, reinforced with reminiscences of his own militant past. 'It may have been a long time ago, but I haven't forgotten what's a big crowd and what's a small crowd,' he said. 'That protest is not a big crowd. They said they were going to get people in by the busload. If they'd asked me, I could have done a much better job.' To which, the American part of the double act chimed in: 'I'm glad they didn't!'

Her comments on Iraq ('the big decision was right') and Guantánamo ('we don't want to be the world's jailers' and will be 'glad when conditions permit' its closure) helped explain not only Lee's fury. They also suggest why there has been growing concern in recent months among Democratic Party political strategists, especially backers of Hillary Clinton for the 2008 race, at the prospect of Condi Rice as the woman to beat.

In substance, she said nothing startlingly new. She even retreated from a remark during a BBC-sponsored debate on Friday that America had made 'thousands' of tactical errors in pursuing a 'correct' strategy in Iraq. 'I meant it figuratively,' she said. 'I wasn't counting.'

But in tone Rice in Liverpool and Blackpool struck at least the placardless among her hosts as more emollient, open, likeable, and thus more effective, than other top US spokesmen.

One of the Muslim leaders said after meeting the Secretary of State that she seemed genuinely to listen, and that even though they had no illusions that their concerns would lead to a change in US policy they appreciated the simple fact that she had come along and done so.